/**
 * Created with IntelliJ IDEA
 * Description:
 * User: Administrator
 * Data: 2023 - 09 - 16
 * Time: 17:15
 */
//牛客 矩阵的最小路径和
public class Solution5 {
    public int minPathSum (int[][] matrix) {
        int m = matrix.length;
        int n = matrix[0].length;
        int[][] dp = new int[m + 1][n + 1];
        for (int i = 0; i <= m; i++) dp[i][0] = Integer.MAX_VALUE;//填dp表时，要保证多加出来的行和列(为防止越界而虚拟出来的格子)里面的值不会影响后面填表的正确性
        for (int j = 0; j <= n; j++) dp[0][j] = Integer.MAX_VALUE;
        dp[0][1] = dp[1][0] = 0;
        for (int i = 1; i <= m ; i++) {
            for (int j = 1; j <= n ; j++) {
                dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + matrix[i - 1][j - 1];//注意下标的映射关系，matrix[i-1][j-1]的下标要用i-1和j-1
            }
        }
        return dp[m][n];
    }
}
